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Let a,b,c be distinct non- negative ...

Let a,b,c be distinct non- negative numbers . If the vectors `ahat(i) + ahat(j) + chat(k) , hat(i) + hat(k) " and " chat(i) + c hat(j) + bhat(k)` lie in a plane then c is

A

the arithmetic mean of a and b

B

the geometic mean of a and b

C

the harmonic mean of a and b

D

equal to zero

Text Solution

Verified by Experts

The correct Answer is:
B
Since three vectors are coplanar .
`|{:(a,,a,,c),(1,,0,,1),(c,,c,,b):}|=0`
Applying `C_(1) to C_(1)-C_(2) , |{:(0,,a,,c),(1,,0,,1),(0,,c,,b):}|=0`
` rArr - 1 (ab -c^(2)) =0 rArr ab = c^(2)`
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